LINEAR THERMO-VISCO-ELASTIC WAVE PROPAGATION INCLUDING STRESS RELAXATION: A GENERAL FRAMEWORK AND CANONICAL PROBLEMS

UoM administered thesis: Phd

Abstract

This thesis is focused around the theoretical study of attenuation of acoustic and elastic waves due to viscous and thermal effects. The initial focus is on fluid acoustic media, where we employ the well known theory of linear thermo-visco-acoustics (TVA) to study the influence of boundary layer effects on the propagation of sound in narrow channels filled by air and water. In the latter case, the effects of fluid-structure interaction are taken into account by assuming the neighbouring solid is elastic, but only acoustically hard solids are analysed. On an attempt to generalise the type of media in consideration, the possible advantages arising from the development of a theory for thermo-visco-elasticity (TVE) in this context are noticed. We propose a TVE framework which incorporates more general material behaviour such as creep compliance and stress relaxation, and can be reduced to several other physically relevant theories like TVA for Newtonian fluids, in a way that we can accurately study a diverse class of materials ranging from metals and polymers to air and water in a large number of conditions. As for TVA fluids, TVE media accept three families of modes in free-space, namely two coupled thermo-compressional waves and a shear wave whose phase speed and attenuation differ significantly depending on the specific material. Accurate asymptotic approximations to thermo-compressional coupling are provided which highly simplify the initial expressions for the wavenumbers. We consider a canonical scattering problem consisting of a compressional plane wave incident on two TVE half-spaces in perfect contact, where the thermo-viscous effects on reflection/transmissions and conveniences of the developed framework as opposed to standard approaches in the literature are highlighted. We make use of the above framework to extend the initial study by examining fluid-filled slits within soft viscoelastic media, which we find gives rise to very different results to those obtained for hard solids in the initial work. We show that this can partly be attributed to the properties of the Scholte mode which propagates in the interface of a fluid-solid half-space and is analysed thoroughly. Particular emphasis is put on how the stress relaxation effects can influence the results, which we find to be significant under certain conditions that are discussed in detail. Furthermore, given the generality of the framework, we can analyse the problem of fluid-loaded viscoelastic plates under the same set of dispersion equations obtained for the slit. In particular, we find that for sufficiently soft media so that the phase speed of the symmetric coupled plate-Scholte mode becomes dispersive, the mode experiences a global maximum in attenuation which may be of physical interest, particularly if stress relaxation can be exploited.

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Original languageEnglish
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Award date1 Aug 2022